Answered

Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies. Follow the models above.

A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41°. How tall is the lighthouse?

A.45.3 yards

B.52.2 yards

C.39.4 yards

Verified Answer :

bcalle

In reference to the angle of elevation (41 degrees), the adjacent side is 60 and the opposite side is the unknown.
Using tangent ratio:
tan 41 = opp/60
60 tan41 = opp
opp side = 52.2yards
LETTER B

Answer: B. 52.2 yards

Lighthouse is 52.2 yards tall.

Step-by-step explanation:

Let AB denotes the height of the lighthouse & BC denotes the distance between the base of a lighthouse and Photographer.

In Figure,  ∠ACB = 41° & ∠ABC = 90°, Threrefore,  Base is BC and perpendicular is AB.

As we know, tan(∠ACB) = \(\frac{Perpendicular}{Base}\)

∴  tan 41° = \(\frac{AB}{BC}\)

tan 41° = \(\frac{AB}{60}\)

0.869286737 = \(\frac{AB}{60}\)

AB = 52.2 yards ( approx.)

Thus, Height of the lighthouse is 52.2 yards


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